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Calcul de l'espérance de la solution d'une EDP stochastique unidimensionnelle à l'aide d'une base réduite

Jocelyne Erhel 1 Zoubida Mghazli 2 Mestapha Oumouni 1, 2 
1 SAGE - Simulations and Algorithms on Grids for Environment
Inria Rennes – Bretagne Atlantique , IRISA-D1 - SYSTÈMES LARGE ÉCHELLE
2 EIMA - Equipe d'Ingénierie MAthématique [Kenitra]
Département de Mathématiques [Kénitra]
Abstract : In this Note, we present an efficient method to approximate the expectation of the response of a one-dimensional elliptic problem with stochastic inputs. In conventional methods, the computational effort and cost of the approximation of the response can be dramatic. Our method presented here is based on the Karhunen-Loève (K-L) expansion of the inverse of the diffusion parameter, allowing us to build a base of random variables in reduced numbers, from which we construct a projected solution. We show that the expectation of this projected solution is a good approximation, and give an a priori error estimate. A numerical example is presented to show the efficiency of this approach.
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https://hal.inria.fr/hal-00782459
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Submitted on : Tuesday, January 29, 2013 - 5:26:36 PM
Last modification on : Wednesday, February 2, 2022 - 3:57:08 PM

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Jocelyne Erhel, Zoubida Mghazli, Mestapha Oumouni. Calcul de l'espérance de la solution d'une EDP stochastique unidimensionnelle à l'aide d'une base réduite. Comptes Rendus. Mathématique, Académie des sciences (Paris), 2011, 349 (15-16), pp.861-865. ⟨10.1016/j.crma.2011.07.015⟩. ⟨hal-00782459⟩

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